Séminaire Lotharingien de Combinatoire, 78B.36 (2017), 12 pp.
Henri Mühle and Philippe Nadeau
The Alternating Group Generated by 3-Cycles
We investigate the partial order on the alternating group generated by
all 3-cycles. We first describe the cover relations in this poset.
Permutations with odd cycles occur naturally, and we study the lower
intervals they induce. These intervals are naturally embedded in the
lattices of noncrossing partitions, and we provide several enumeration
formulas for them. We also study the natural action of the braid
group on the maximal chains in any given interval, and determine when
this action is transitive. We also outline the many ways in which our
construction can, or could, be extended.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
The following versions are available: